Title: All entangled quantum states are nonlocal: equivalence between locality and separability in quantum theory

Abstract:

In this talk I will show how, by slightly modifying the rules of nonlocal games, one can prove that all entangled states violate local realism.

As it is well known, Bell inequalities, which are used to test the violation of local realism, can be equivalently reformulated in terms of nonlocal games (namely, cooperative games with incomplete information) played between one referee and two (or more) players, these latter being separated so to make any form of communication between them impossible during the game. Quantum nonlocality is that property of quantum states that allows players sharing them to win nonlocal games more frequently than the assumption of local realism would imply.

However, as Werner proved in 1989, not all quantum states enable such a violation of local realism. In particular, Werner showed the existence of quantum states that cannot be created locally (the so-called “entangled” states) and, yet, do not allow any violation of local realism in nonlocal games. This fact has been since then considered an unsatisfactory gap in the theory, attracting a considerable amount of attentions in the literature.

In this talk I will present a simple proof of the fact that all entangled states indeed violate local realism. This will be done by considering a new larger class of nonlocal games, which I call “semiquantum,” differing from the old ones merely in that the referee can now communicate with the players through quantum channels, rather than being restricted to use classical ones, as it was tacitly assumed before. I will then prove that one quantum state always provides better payoffs than another quantum state, in semiquantum nonlocal games, if and only if the latter can be obtained from the former, by local operations and shared randomness (LOSR). The main claim will then follow as a corollary.

The new approach not only provides a clear theoretical picture of the relation between locality and separability, but also suggests, thanks to its simplicity, new experimental tests able in principle to verify the violation of local realism in situations where previous experiments would fail.